Penalty-based continuous aggregation operators and their application to group decision making

Penalty-based aggregation operators, which are obtained by minimizing the deviation between the input values and the aggregated value, have a direct intuitive interpretation in terms of practical problems. In order to aggregate continuous interval arguments based on penalty, we present penalty-based continuous (PC) aggregation operators, and investigate some desirable properties of them. When different forms of the associated dissimilarity function are employed, various continuous aggregation operators can be deduced, such as the C-OWA operator and the QC-OWA operator. Moreover, several extensions of the PC aggregation operators are developed for the aggregation of multiple interval arguments. Finally, we apply these aggregation operators to developing an approach to multi-attribute group decision making. A numerical example is illustrated to show the feasibility and effectiveness of the developed approach.